Methods and kits for screening nucleic acid duplex stability

ABSTRACT

Simple methods and kits for determining thermodynamic stability of nucleic acid duplexes and single polynucleotide polymorphisms via competitive equillibria are provided.

This application claims the benefit of provisional application No.60/113,731 filed Dec. 23, 1998 and 60/119,909 filed Feb. 12, 1999.

INTRODUCTION

This invention was made in the course of research sponsored by theNational Institutes of Health. The U.S. Government may have certainrights in this invention.

BACKGROUND OF THE INVENTION

Mutagenic lesions in DNA frequently result from structural modificationsof the heterocyclic bases (exocyclic adducts, free radical-inducedmodifications) and/or from complete removal of the base (abasic sites).Further, cellular processing of lesion containing DNA can lead tomismatches, additions, deletions or base pair substitutions. Thus, bylesion, it is meant to include mismatches, additions and deletions. Awide range of lesion-induced thermodynamic effects have been observed.Typically, the free energy stabilizing the duplex is reducedsignificantly by inclusion of the lesion. Methods of determining lesioneffects on duplex free energy are limited. Typically, the effect of aDNA modification on the energetics of duplex formation is measured bycomparison of independently measured association constants for themodified and unmodified duplex or by comparing Tm values, which arecommonly but erroneously believed to represent thermodynamic stability.Therefore, there is a need for a simple, reproducible and sensitivemethod for rapidly screening for duplex stability.

The assays of the invention have two novel features which, whencombined, provide a powerful and rapid method to assess the consequencesupon duplex formation of perturbations to localized and/or globalchemical features of nucleic acids. The first unique aspect is using twosimultaneously competing equilibria to identify differences inequilibrium constants, between formation of two different nucleic acidduplexes. Typically, the effect of a DNA modification on the energies ofduplex formation have been measured by comparison of independentlymeasured association constants for the modified DNA and the unmodifiedduplex requiring two separate experiments. A second novel feature of thepresent invention is that these assays require only one experiment.

Furthermore, there is a large technical barrier for direct measurementof single duplex association events. In conventional titrationexperiments, a solution of one strand is added to a solution of itscomplement with formation of a duplex monitored by any of a variety ofmethods, including spectroscopic and calorimetric methods. To extractuseful information from a conventional titration, the experiment must bedevised such that a significant fraction of free titrant will be presentthroughout the titration. Satisfaction of this condition leads to thefamiliar sinusoidal shape of the titration curve. To satisfy thiscondition, typically the product of the initial titrate concentration,c, and the association constant, K, is in the range 10<cK<1000. Due tothe high association constant for nucleic acid duplexes, the componentconcentration must be below the association constant, the components arelikely to be too dilute to be detected by standard spectroscopic means.Having nucleic acids compete for duplex formation, as in the presentmethod, creates a second equilibrium, referred to herein as a“competition” for duplex formation, that is measurable at essentiallyany concentration range. Thus, the concentrations can be tailored tovirtually any method of detection. Further, the competition is measureddirectly from a single experiment rather than having to compare theresults of two independently measured experiments.

Another innovative aspect of this invention is the ability todiscriminate between the two duplexes being formed. In one embodiment ofthe present invention fluorescence energy transfer is used to facilitatethis discrimination. A common spectroscopic method for monitoring duplexformation relies on the hyperchromicity of duplex formation. However,the extinction coefficients of duplexes of similar length is not a verysensitive reporter of the small differences in DNA content that are ofmost interest, as in the case of oligonucleotide duplexes with damage toonly a single base. Even a technique such as circular dichroism is notsufficiently sensitive and also suffers from difficulties ininterpretation of spectral variation which can be due to factors otherthan duplex formation. FET provides a unique, extremely sensitive, andessentially binary means of discrimination because only a duplex withboth the donor and acceptor dyes will have the spectroscopic signatureof the energy transfer.

Competitive equilibrium assays of the present invention are more widelyadaptable to a variety of nucleic acid systems than are assays that arebased on changes in intrinsic spectral characteristics of the dyes. Forexample, the FET assay of the invention is dependent only on thepresence of the two dyes and is limited only by the necessity ofmodifying DNA to bear the dyes and the fact that the distance betweenthe dyes increases substantially when the initial FET duplex isdisrupted. Any spectral changes that accompany the disruption of the FETduplex can be easily treated during data analysis and do not cause anysignificant complication for the FET assay.

Thus, the present invention has a number of significant advantages overprior art techniques for determining duplex stability.

SUMMARY OF THE INVENTION

An object of the present invention is to provide methods for screeningfor nucleic acid duplex stability by competitive equilibria. In thesemethods, a solution is first produced containing a known amount of aninitial or reference nucleic acid duplex with a known stability. Theinitial duplex is comprised of a first nucleic acid strand having asequence, wholly or in part, homologous to a target strand and a secondnucleic acid strand having a sequence, wholly or in part, complementaryto the target strand. A series of additions of target strand are thenmade by titrating the solution with a second solution comprising a knownconcentration of the target nucleic acid strand. This target nucleicacid strand competes with the first nucleic acid strand for binding to anucleic acid strand of the initial nucleic acid duplex. After eachaddition or titration, the solution is subjected to conditions whichdisrupt some or all of the nucleic acid duplexes and triplexes in thesolution; subjected to conditions which promote duplex or triplexformation, and then monitored for any changes in the amount of initialnucleic acid duplex formed as a function of the amount of target nucleicacid strand added. This method can be used for extracting enthalpy databy controlling temperature during duplex or triplex formation andmonitoring changes as a function of temperature so that a family oftitration curves can be made and used to extract enthalpy (ΔH°) data.

Another object of the present invention is to provide a for detecting asingle nucleotide polymorphisms. In this embodiment of the invention,the initial nucleic acid duplex comprises a first and second nucleicacid strand, wherein the first or second strand of the duplex isdesigned to identify a single nucleotide polymorphism in a single- ordouble-stranded target nucleic acid sequence. In this method, the amountof the initial nucleic acid duplex in a solution is first determined. Afixed excess amount of a target nucleic acid strand is then added to thesolution. The solution is then subjected to conditions which disruptsome or all duplexes or triplexes in the solution followed by conditionswhich promote duplex or triplex formation. The amount of initial duplexformed after addition of the target strand is then measured. Thismeasured amount, after addition of the target strand, is indicative ofthe target strand containing the single nucleotide polymorphism.

Another object of the present invention is to provide methods fordetermining the concentration of a target nucleic acid strand whichcomprises adding a known volume and concentration of an initial nucleicacid duplex with a known stability to a known volume of a solutioncontaining a target strand. Alternatively, a known volume of a solutionof target strand can be added to a known volume of a solution containinga known concentration of an initial nucleic acid duplex with a knownstability. The solution is then subjected to conditions which disruptthe initial nucleic acid duplex and any duplex between the target strandand a strand of the initial nucleic acid duplex followed by conditionswhich promote duplex formation. The relative change in the amount ofinitial duplex formed in the solution after addition of the targetstrand is used to determine concentration of the target strand.

Another object of the present invention is to provide a method forassessing stability of various selected target strands. In this methodcompetitive equilibrium assays are performed with the same initialnucleic acid duplex for each selected target strands. Changes in theamount of initial nucleic acid duplex formed as a function of the amountof the selected target nucleic acid strand added are compared for eachtarget strand to ascertain differences in stability of duplexes ortriplexes formed by the various target strands. In this embodiment ofthe invention it is not necessary to know the stability of the initialnucleic acid duplex.

In a preferred embodiment of these methods of the invention, the firstnucleic acid strand comprises a donor nucleic acid strand labeled with adonor of a FET pair and the second nucleic acid strand comprises anacceptor nucleic acid strand labeled with an acceptor of the FET pairand changes in the amount of initial nucleic acid duplex in the titratedsolution are monitored by measuring changes in FET donor or acceptorintensity.

Yet another object of the present invention is to provide kits forscreening for nucleic acid duplex stability and single nucleotidepolymorphisms by competitive equilibria methods.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is a method and kit for screening the impact onnucleic acid duplex stability of alterations in base structures, e.g.due to carcinogen exposure or synthetic modification; the role ofsequence context on such effects; and any other such alterations inWatson-Crick pairing such as mismatched base pairs or bulged/unpairedbases. Modifications of the phosphodiester backbone may also bedetected. The small amounts of material required, speed of execution andapplicability to a wide range of test strands make the assay useful fordetailed thermodynamic characterizations and for screening applications.These features make the methods and kits of the present inventionsuperior to calorimetry and other optical methods, with significantsavings in the amount of test material necessary to perform a freeenergy determination. The range of effects on duplex stability of aparticular defect or modification can be readily determined with themethods of the invention. With this information, the most interestingduplexes can be identified for further study. Thus, large investments intime and materials will be made only for systems of real interest.

One of the key features of the invention is the flexibility in thenature of the test nucleic acid components that can be evaluated. In oneexperiment, two 13 mer DNA oligonucleotides, each bearing one of the FETfluorophores, referred to herein as donor (D) and acceptor (A) strands,form a duplex. The test or target strand competitor is a third DNAoligonucleotide of the same length bearing a single damaged site at thecentral position. However, application of the method is general,encompassing virtually any variation in the nature of the nucleic acidduplex and test strand competitor. The donor (D) and acceptor (A)strands need not be the same length nor must the target, whether singlestrand or duplex. Further, as used herein, the terms “DNA”, “nucleicacid”, “oligonucleotide” and “strand” are meant to include othervariations as there is no requirement for any of the three nucleic acidstrands to be DNA. Accordingly, the terms “DNA”, “nucleic acid”,“oligonucleotide” and “strand” are meant to include DNA, RNA, andanalogues including those comprised, in whole or in part, of modifiedbases and/or modified backbones such as peptido-nucleic acids (PNA) andother oligomers, incorporating modified phosphate and/or sugar moieties(e.g. PNAs, methyl phosphonates, phosphorothioates) that maintainduplex-forming ability may be used in the method of the invention.Further, these terms are also inclusive of the vast number ofnon-Watson-Crick nucleotide base variations that may be incorporatedinto any of the components, including intra strand crosslinks, abasicsites, naturally occurring or synthetic base variants, base mimetics andbase adducts, including, for example, carcinogen-induced adducts. Thereis also no need to limit the system to three independent strands of thesame length competing for formation of two possible duplexes.

Most nucleic acid amplification techniques, such as polymerase chainreaction produce duplex target. The technique of the present inventioncan be used on such targets in one of two ways.

In a first embodiment, a triple helix is formed between the targetduplex and one of the strands of the reference duplex. The sequencerequirements for triple helix formation are well known. Typically,triple helices involve stretches of pyrimidines on one strand of aWatson-Crick duplex, a complementary stretch of purines on the otherstrand of the Watson-Crick duplex, and a third strand comprised ofstretches of either complementary purines or pyrimidines which residesin the major groove of the duplex. Details of the sequence requirementsand tolerated substitutions are well known and widely described in theart. The target duplex need not be disrupted and all calculationequations provided in the Examples are applicable to this embodimentwithout modification.

The second embodiment is more complex and applicable only when sequencesdo not meet the requirements for triple helix formation. In thisembodiment, the target duplex must be disrupted, i.e. melted, so thatboth the donor-labeled and acceptor-labeled oligonucleotide can bind tothe complementary strand of the target duplex. The addition of twoequilibria (the formation of the target duplex and the interaction ofthe donor strand with one of the target duplex strands) makes thisformalism inappropriate for deriving quantitative data. However, due tothe law of mass action, the equilibrium distribution of complexes willstill depend on the relative values of the equilibrium associationconstants and the various concentrations. Therefore, the FET observablewill also depend on these values. As a consequence, qualitativeinformation on the relative stability of complexes formed by the targetduplex's component strands and various sets of DNA duplex probes can beobtained.

The method is also useful for structures that might include largebulging/unpaired regions, competing internal loops and/or hairpins orother deviations from simple duplex formation. The above-mentionedvariants may occur in combination, thereby increasing the number ofpotential targets of study.

The only limitations are that the FET donor and acceptor be withinresonance distance in the initial duplex and that formation of thecompeting complex prevents energy transfer by displacement of eitherdonor or acceptor. Any FET donor and acceptor pair can be used and suchdyes are well known in the art and commercially available. Thefluorescent dyes may be at opposite ends of the duplex (−5′ and −5′ or3′ and 3′), the same end of the duplex (−5′ and −3′), or with one orboth fluorophores in the interior of the strand(s). The fluorophores maybe linked after oligonucleotide synthesis or, when the phosphoramiditesare available, incorporated during synthesis.

Further, FET, monitored either by fluorescence of the acceptor or byquenching of the donor, is not the only usable means of monitoring theamount of the reference or donor-acceptor duplex. Any method by whichthe amount of reference or initial duplex can be monitored as a functionof the amount of target can be used. Eximer fluorescence or otheroptical means can be used. In fact, nucleic acid strands of the initialduplex can be labeled with any pair of species with properties orcharacteristics dependent upon proximity. Examples include, but are notlimited to, fluorescent dyes, antibody-antigen pairs, enzyme-inhibitorpairs and enzyme-coenzyme pairs. Further, if the assay is carried out ona surface, surface plasmon resonance (SPR) spectroscopy may be employedwith the label being a chromophore at the wavelength used in the SPRmeasurement.

The high throughput nature of this assay, in comparison to the more timeand material intensive techniques generally used for thermodynamicanalysis, makes the assay applicable to various problems inbiotechnology and pharmaceutical research. For example, this assay canbe used to evaluate nucleotide mimetics as drugs such as the anti-HIVdrugs ddC and AZT; to evaluate the effects of carcinogen/chemicalexposure on the stability of DNA and DNA-RNA hybrid duplexes; and forscreening of various parameters for hybridization studies (e.g.temperature, buffer, sequences). Screening of non-natural nucleic acidanalogs as antisense or antisense agents can also be addressed by thismethod. The assay of the invention can be a companion technique to helpimprove existing hybridization techniques. The method of the inventioncan also be used for screening, in solution, for the presence of singlenucleotide polymorphisms (SNPs or “snips”) which are used inpharmacogenetic research targeted at identifying the genetic basis ofdisease and genetic diagnosis of the potential for such disease inindividuals. The latter aspects have particular importance in thebiotechnology industry. Many companies are currently involved indeveloping and marketing hybridization assays for a wide variety ofresearch and development efforts. Virtually all of the assays currentlyin use rely on immobilization of at least one participant in thehybridization reaction. Significantly, the immobilization introduces ahost of complications, including non-specific interaction of any/all ofthe components with the immobilizing platform; possible distortion ofthe biochemically important equilibrium due to immobilization; thepossibility that the chemical linkage of the immobilization canpartially occlude the necessary interactions with the non-immobilizedcomponents; and the necessity of additional steps in the protocol forthe immobilization itself prior to running the binding experiments. Themethod of the invention, being entirely in solution, eliminates thecomplications caused by immobilization. Further, because the method usestitration, control experiments with standardized DNA can be runfrequently or in parallel with test compounds to eliminate spuriousresults. Such standardized DNA is a component of a kit for carrying outthe method of the invention.

The competing equilibria which are the basis of this assay provide agreatly enhanced method for detecting differences in stability betweentwo nearly identical duplexes. Studying the association of two strandsforming one duplex and comparison of the association of two otherstrands in a separate experiment, as is done in current methods,requires two experiments with the inherent compounding of experimentalerror. The present invention advantageously requires only one.

The calculations used for data analysis are derived from the generalequations for three component, two-equilibria systems as taught by Linnand Riggs (J. Mol. Riol. (1972), 72, 671-90).

Two equilibrium association constants are defined below, with subscriptsf and t indicating free and total concentrations, respectively, and AD,AX, D, A, and X represent the donor/acceptor complex, thecompetitor/acceptor complex, donor strand, and acceptor strand, and thecompetitor or “test” strand, respectively: $\begin{matrix}{K_{AX} = {\frac{\left\lfloor {AX} \right\rfloor}{{\lbrack X\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {AX} \right\rfloor}{\left( {\lbrack X\rbrack_{t} - \lbrack{AX}\rbrack} \right)\left( {\lbrack A\rbrack_{t} - \lbrack{AD}\rbrack - \lbrack{AX}\rbrack} \right)}}} & \left( {{Equation}\quad 1} \right) \\{K_{AD} = {\frac{\left\lfloor {AD} \right\rfloor}{{\lbrack D\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {AD} \right\rfloor}{\left( {\lbrack D\rbrack_{t} - \lbrack{AD}\rbrack} \right)\left( {\lbrack A\rbrack_{t} - \lbrack{AD}\rbrack - \lbrack{AX}\rbrack} \right)}}} & \left( {{Equation}\quad 2} \right)\end{matrix}$

These equations are for the “test” or “target” strand forming a complexwith the acceptor strand. In this and the models that follow, theopposite competition, with X binding to D, can also be described bysimple substitution of the terms.

These basic expressions for the equilibrium constants can be combinedand rearranged to the following equation: $\begin{matrix}{\lbrack{AD}\rbrack = \frac{\left\lfloor A \right\rfloor_{t}\left( {\left\lfloor D \right\rfloor_{t} - \left\lfloor {AD} \right\rfloor} \right)}{\frac{1 + {\left( {\lbrack X\rbrack_{t} - \lbrack{AX}\rbrack} \right)K_{AX}}}{K_{AD}} + \left( {\lbrack D\rbrack_{t} - \lbrack{AD}\rbrack} \right)}} & \left( {{Equation}\quad 3} \right)\end{matrix}$

The loss of energy transfer is monitored as the AD complex is disruptedby the formation of AX. The complementary measurement of emission of theacceptor subsequent to energy transfer also may be used. Which approachworks better will depend on the photophysical properties of thefluorescent dyes. As discussed, the value, θ is the fraction of theinitially observed fluorescence energy transfer at each point in thetitration and is related to the relative concentrations of thedonor/acceptor complex ([AD]) to [total donor strand] ([D]_(t))([AD]=[D]_(t) at the beginning of the titration): $\begin{matrix}{\theta_{n} = {\frac{\lbrack{AD}\rbrack}{\lbrack D\rbrack_{t}} = \frac{I_{D} - I_{n}}{I_{D} - I_{AD}}}} & \left( {{Equation}\quad 4} \right)\end{matrix}$

with relative fluorescence readings for the dilution-corrected relativefluorescence at each point n, I_(n), fluorescence of the fully formedPET duplex, I_(AD), and the fluorescence of the donor strand alone,I_(D).

In equation 5, the dilution corrections are added explicitly, whereV_(o) is the initial volume of the D-containing solution, V_(A), thevolume of the added A-containing solution, and v₁, the volume of the ithaliquot of the X-containing solution. $\begin{matrix}{\theta_{n} = \frac{I_{D} - {I_{n}\left( \frac{V_{n} + V_{A} + {\sum\limits_{i = 1}^{n}V_{i}}}{V_{D}} \right)}}{I_{D} - {I_{AD}\left( \frac{V_{D} + V_{A}}{V_{D}} \right)}}} & \left( {{Equation}\quad 5} \right)\end{matrix}$

Substituting Equation 3 into Equation 4, assuming that [X]_(t)>>[AX],and rearranging yields Equation 6. $\begin{matrix}{\theta = \frac{\left\lfloor A \right\rfloor_{t}\left( {1 - \theta} \right)}{\frac{1 + {\lbrack X\rbrack_{t}K_{AX}}}{K_{AD}} + {\lbrack D\rbrack_{t}\left( {1 - \theta} \right)}}} & \left( {{Equation}\quad 6} \right)\end{matrix}$

A program (written in the Microsoft VBA language) that computes afunction theta([A]_(t), [D]_(t), [X]_(t), K_(AD), K_(AX)) to calculatethe isotherms (θ vs. X_(t) or logX_(t)) using equation 6 is depicted inExample 5. The value of θ is found by iteration to satisfy the equationRHS(equation 6)−θ=0, where RHS means right-hand side. The entireexperimental isotherm can be fit using equation 6 to find a value forthe desired parameter K_(AX). This is, however, not necessary as shownin the following section.

X_(0.5) is defined as the concentration of competing strand X at whichθ=0.5, or exactly half of the acceptor/donor duplex, AD, has beendisrupted. The value of X_(0.5) can be interpolated from a plot of θversus log[X]_(t). When θ=0.5, a simple relation between the desiredequilibrium constant K_(AX),the measured value X₀ ₅, and the knownvalues [D]_(t) and K_(AD) results in: $\begin{matrix}{K_{AX} = \left( \frac{{K_{AD}\lbrack D\rbrack}_{t}}{2X_{0\quad 5}} \right)} & \left( {{Equation}\quad 7} \right)\end{matrix}$

Application of the well known relation between ΔG° and K yields Equation8: $\begin{matrix}{{\Delta \quad G_{AX}^{\circ}} = {- {{RTn}\left( \frac{{K_{AD}\lbrack D\rbrack}_{t}}{2X_{0 \cdot 5}} \right)}}} & \left( {{Equation}\quad 8} \right)\end{matrix}$

The value of K_(AD) will have been previously determined by independentmethods such as differential scanning calorimetry and UV-absorbancemelting. Alternate representations of equation 8 can be used to evaluatethe free energy changes associated with the formation of the duplexesand the defects. $\begin{matrix}{{\Delta \quad G_{AX}^{{^\circ}}} = {{\Delta \quad G_{AD}^{{^\circ}}} - {{RT}\quad \ln \frac{D_{t}}{2X_{0\quad 5}}}}} & \left( {{Equation}\quad 9} \right) \\{{\Delta \quad G_{AX}^{{^\circ}}} = {{{- {RT}}\quad \ln \quad K_{AD}} - {{RT}\quad \ln \frac{D_{t}}{2X_{0\quad 5}}}}} & \left( {{Equation}\quad 10} \right) \\{{{\Delta \quad G_{AX}^{{^\circ}}} - {\Delta \quad G_{AD}^{{^\circ}}}} = {{- {RT}}\quad \ln \frac{D_{t}}{2X_{0\quad 5}}}} & \left( {{Equation}\quad 11} \right)\end{matrix}$

Alternatively, the impact of a difference between two oligonucleotides(X₁ & X₂) on duplex stability, ΔΔG°, can be evaluated by titration (inseparate experiments) of the two competitors against the same referenceAD duplex at the same AD concentration (Equation 12). $\begin{matrix}{{{\Delta\Delta}\quad G_{1\quad 2}^{{^\circ}}} = {{{\Delta \quad G_{1}^{{^\circ}}} - {\Delta \quad G_{2}^{{^\circ}}}} = {{- {RT}}\quad \ln \left\lfloor \frac{X_{{0 \cdot 5}\quad 2}}{X_{0\quad {5 \cdot 1}}} \right\rfloor}}} & \left( {{Equation}\quad 12} \right)\end{matrix}$

In Equation 12, the value for K_(AD) is canceled. Therefore, one canevaluate the free energy impact of a single defect, or multiple defects,without thorough thermodynamic characterization of the AD duplex.

The assumption of [X]_(t)>>[AX] in equation 6 can be relaxed therebyleading to $\begin{matrix}{\theta = \frac{\left\lfloor A \right\rfloor_{t}\left( {1 - \theta} \right)}{\frac{1 + {\left( {\lbrack X\rbrack_{t} - \lbrack{AX}\rbrack} \right)K_{AX}}}{K_{AD}} + {\lbrack D\rbrack_{t}\left( {1 - \theta} \right)}}} & \left( {{Equation}\quad 13} \right)\end{matrix}$

An unknown parameter [AX] must be evaluated as part of the calculationof θ. This is accomplished by iteration over [AX] with the restrictionthat [A]_(t)=[AX]+[AD]+[A]_(f). A second root finding problem isexecuted with the objective being finding a value of [AX] that satisfiesthe equation $\begin{matrix}{{\lbrack A\rbrack_{t} - \lbrack{AX}\rbrack - {\theta \quad D_{t}} - \frac{\theta}{K_{AD}\left( {1 - \theta} \right)}} = 0} & \left( {{Equation}\quad 14} \right)\end{matrix}$

A second program is also shown in Example 5 that calculatestheta([A]_(t), [D]_(t), [X]_(t), K_(AD), K_(AX)) without the restrictionhat [X]_(t)>>[AX]. While a useful reduction of equation 13 (similar toequations 7 and 8) cannot eliminate the need for iterative solution,values of X_(t) at θ=0.5 are readily calculated. Values of X_(t) socalculated are compared to experimental values and K_(AX) adjusted toproduce the experimental value of X_(t).

Comparison of isotherms calculated using equations 6 and 13 reveal thatthe error introduced by the assumption of negligible [AX] is small andonly significant when K_(AX)˜K_(AD). For K_(AX)/K_(AD)=1, the error infree energy is about 0.4 kcal/mole; for K_(AX)/K_(AD)=0.1, 0.06kcal/mole; and for K_(AX)/K_(AD)=0.01, 0.005 kcal/mole. Therefore, theassumption is in most cases reasonable. Those cases where it is nottotally without adverse consequence, that is where K_(AX)˜K_(AD), arereadily predictable, can be addressed easily by application of the fullequation 13.

As is clear from the equations 7 and 8, the K_(AX) and ΔG°_(AX) valuesthat are measured are relative to the value of K_(AD). As a practicalmatter, titration of X into the solution to a concentration of1000[D]_(t) is convenient. An X_(0.5) value of 1000[D]_(t) correspondsto a ΔΔG° value of about 4.5 kcal/mole (ΔΔG°=−RTln(1/2000). This is arather large range and should accommodate most single base defects. Therange can easily be extended by performing additional titrations usingless stable AD duplexes. The stability of the AD duplexes can bemodulated by inclusion of modified bases and/or mismatches. A series ofAD duplexes can therefore be designed to cover essentially any range ofΔG° values, in intervals of 3 to 4 kcal/mole.

Analysis of the parallel titrations can be accomplished independently orcollectively to determine the free energy values using the analysisdescribed above.

Equation 6 can be rearranged and used to determine the concentration ofa target sequence (X), when the values of K_(AD) and K_(AX) are known.In this example, a known volume and concentration of AD duplex is addedto a known volume of an X containing solution. Alternatively, a knownvolume of X containing solution is added to a known volume of AD duplexcontaining solution of known concentration. Thus [A]_(t)=[D]_(t) isknown. The concentration of X, [X]_(t), can be calculated from therelative change in fluorescence, θ, using the formula $\begin{matrix}{\lbrack X\rbrack_{t} = {\frac{K_{AD}}{K_{AX}}{\left\{ {{\lbrack A\rbrack_{t}\left( {1 - \theta} \right)^{2}} - \theta} \right\}/\theta}}} & \left( {{Equation}\quad 15} \right)\end{matrix}$

When the temperature is controlled during the annealing process of atitration, additional information can be obtained. The cooling processcan be performed in steps so that values of θ are collected as afunction of temperature. Data at each temperature are used to produce afamily of titration curves. Each curve is analyzed independently andvalues for K_(AX) are determined as a function of temperature. The van'tHoff equation,

ΔH°=−R(∂lnk/∂(l/T))  (Equation 16)

can be used to extract enthalpy (ΔH°) data. The thermodynamicdescription, at a given temperature is completed by using ΔG°=−RTlnK andΔS°=(ΔH°−ΔG°)/T.

Direct detection of formation of DNA duplexes by titration is extremelydifficult because of the very low concentrations required for monitoringthe equilibrium which are well below the operating range of traditionalin-solution methods. A competition assay is usable over a wide range ofinstrumentally accessible concentrations. The method of the inventionprovides a more reliable measurement of nucleic acid complex stabilityover a very wide range of free energy values because the titrationdepends on the difference in stability between the initialdonor/acceptor-containing duplex and the resulting competitor-containingduplex and not on their absolute free energy values. Therefore, therange of accessible free energy values can be tuned by choice of theinitial donor/acceptor-containing duplex. Relative free energies areusually the desired experimental result and the method of the inventionprovides them directly. The lower detection limits of the fluorophoresdefine the maximum difference in free energy that can be detected by themethod. The use of fluorophore detection provides great sensitivity. Theemission spectrum of the donor strand at 10 pM concentration has beenvisualized reliably using a photon-counting fluorometer.

Free energies calculated from the assay of the present invention havebeen demonstrated to be in agreement with those measured by extensivethermodynamic studies on individual duplexes. In these experiments, twotitrations were performed at the same D_(t) concentration, for twostarting Watson-Crick FET duplexes, designated A·T and T·A, which differonly by the central base pair, out of the 13 pairs in the duplex.Competition on each duplex is from nearly the same single strand aspresent in the FET duplexes, except this single strand is unlabeled andhas a tetrahydrofuranyl abasic “lesion” site (F) at the central basepair. Free energy values measured by this method compare quite favorablyto those measured by extensive differential scanning calorimetry and UVabsorbance melting experiments on these 13-mer duplexes containing asingle tetrahydrofuranyl abasic site (F) in the central position.Specifically, using the FET assay, a value of −14.5±0.1 kcal/mole forformation of the F·T duplex was determined, compared with a value of−15.1±0.6 kcal/mole determined using DSC/UV melts. Similarly, using theFET assay a value of −16.2±0.1 kcal/mole was determined for formation ofthe F·A duplex compared with a value of −16.0±0.4 kcal/mole by DSC/UVmelts. These results correspond to ΔΔG° values of −1.7±0.2 kcal/molefrom FET and −0.9±1.0 kcal/mole from DSC/UV melting studies forsubstitution of an A residue for a T residue opposite the abasic site.

Because measurement depends on relative concentration, [D]_(t)/[X], themethod of the present invention can be used in any concentration regime.The appropriate concentration range is determined by the sensitivity ofthe detection system. Accordingly, [D]_(t) is selected by one of skillto optimize the detection method. Due to practical limitations on thevolume of titrant that can be added to the titrate, there are somepractical limitations to the range of free energy values that can becovered by a single titration. However, this range is quite large. Aconvenient limit of the ratio [D]_(t)/[X]_(0.5) is about 0.001. Thiscorresponds to a factor of about 0.002 in association constant or 3.7kcal/mol in free energy. Most defects for which reliable free energydata are available fall into this range.

However, since the measured free energy values depend on the ratio ofK_(AD) and K_(AX) (ΔΔG°), the appropriate choice of donor-acceptorduplex must be made for each titration. Because the complementarity ofthe component strand of the donor-acceptor reference duplex need be onlysufficient to form the duplex and achieve moderate thermal stability,the assay may be tuned over a wide range of free energy values byintroducing mismatches in the donor-acceptor reference duplex. Byjudicious choices of donor-acceptor duplexes, a series of three donoracceptor duplexes can cover a range of 11 kcal/mole in free energy. Iftitrations are done in parallel, use of such a family of duplexesrelieves one of estimating the magnitude of K_(AX) prior to performingthe titration. In this embodiment of the method of the presentinvention, several donor/acceptor complexes are formed simultaneously.Each different donor or acceptor oligonucleotide differs slightly, whilemaintaining complementarity of the acceptor with the target (X) oremploying an analogous system where X binds to the donor, to producedonor/acceptor pairs of differing stability. By appropriate selection ofdonor and acceptor dyes, it is possible to conduct multiple simultaneoustitrations of X into a single solution. Spectroscopic discrimination ofthe various donor acceptor pairs provides multiple free energydeterminations simultaneously.

The assay of the present invention can be adapted by immobilization to avariety of inert solid supports using technologies established forstandard hybridization studies. In this embodiment, one of the strandsof the reference duplex (either donor(D) or acceptor (A)) can beattached to the surface. The reference duplex can then be formed on thatsurface. Exposure to target will release the unattached strand, therebyproducing the signal. Because concentration cannot be defined at asurface in the same way as in solution, comparison to a standard ofknown stability is required for quantitative results. However,immobilization facilitates the miniaturization and adoption of thisassay to high throughput screening while providing the benefit of usingFET and the competing equilibria to increase the sensitivity ofmeasurement of differences in duplex stability. Immobilization may alsoallow for the construction of an array of donor/acceptor duplexes ofdiffering stability. Such an array assures appropriate selection of theinitial complex. Further, because ranges of the free energy differencesmeasurable using the various initial complexes overlap, multiplecomplementary measurements can be made simultaneously.

Simultaneous titrations provide a number of additional advantages tothis assay. With appropriately designed donor-acceptor referencecomplexes, the range of accessible free energy is multiplied by thenumber of duplexes titrated simultaneously. Thus, employing threesimultaneous donor-acceptor duplex titrations means that the effectiverange of a single titration experiment becomes 9-12 kcal/mol, withoutexpending any extra test strand. The enhanced range also means that afavorable outcome is likely in a single experiment, rather than havingto explore various single donor acceptor duplexes to find one which hasa free energy less than 3-4 kcal/mol higher than the test duplex.Second, this application provides a degree of multiplexing that reducesthe time involved in each assay, and thereby enhances the ability toperform high throughput screening of nucleic acid variations. Thus, thesimultaneous titrations are truly simultaneous rather than merely inparallel, meaning that all of the information is gathered using a singlecuvette. The detailed theory supporting the simultaneous titrationexperiment is described below.

Single Acceptor/Multiple Donor or Multiple Acceptor/Single Donor Method

In principle, any number of donor-acceptor pairs could be included withselective excitation of the donors and a single acceptor. The limitationis imposed by the necessity of finding several donors withnon-overlapping excitation spectra and sufficient Stokes shifts suchthat their emission spectra each overlap sufficiently the excitationspectrum of the acceptor. This method allows a series of AD complexeswith varying K_(AD) to be used simultaneously.

As an example, the case wherein there are 3 donors (D₁, D₂, D₃) and asingle acceptor dye (A) is described; however, the number of donors isnot limited to 3. The donors are discriminated by the excitationwavelengths, λ₁, λ₂, λ₃. The initial concentrations are[D₁]_(t)=[D₂]_(t)=[D₃]_(t)=[A]_(t)/3. The Donor and acceptor labeledstrand can form any or all of the complexes AD₁, AD₂, AD₃, and AX. Theequilibrium constants for the various complexes that form are enumeratedbelow. $\begin{matrix}{K_{{AD}_{1}} = {\frac{\left\lfloor {D_{1}A} \right\rfloor}{{\left\lbrack D_{1} \right\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {D_{1}A} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{1} \right\rbrack_{t} - \left\lbrack {D_{1}A} \right\rbrack} \right) \\\left( {\lbrack A\rbrack_{t} - \left\lbrack {D_{1}A} \right\rbrack - \left\lbrack {D_{2}A} \right\rbrack - \left\lbrack {D_{3}A} \right\rbrack - \lbrack{AX}\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 17A} \right) \\{K_{{AD}_{2}} = {\frac{\left\lfloor {D_{2}A} \right\rfloor}{{\left\lbrack D_{2} \right\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {D_{2}A} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2} \right\rbrack_{t} - \left\lbrack {D_{2}A} \right\rbrack} \right) \\\left( {\lbrack A\rbrack_{t} - \left\lbrack {D_{1}A} \right\rbrack - \left\lbrack {D_{2}A} \right\rbrack - \left\lbrack {D_{3}A} \right\rbrack - \lbrack{AX}\rbrack} \right)\end{matrix}}}} & \text{(Equation~~17B)} \\{K_{{AD}_{3}} = {\frac{\left\lfloor {D_{3}A} \right\rfloor}{{\left\lbrack D_{3} \right\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {D_{3}A} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{3} \right\rbrack_{t} - \left\lbrack {D_{3}A} \right\rbrack} \right) \\\left( {\lbrack A\rbrack_{t} - \left\lbrack {D_{1}A} \right\rbrack - \left\lbrack {D_{2}A} \right\rbrack - \left\lbrack {D_{3}A} \right\rbrack - \lbrack{AX}\rbrack} \right)\end{matrix}}}} & \text{(Equation~~17C)} \\{K_{AX} = {\frac{\left\lfloor {AX} \right\rfloor}{{\lbrack X\rbrack_{f}\lbrack A\rbrack}_{f}} = \frac{\left\lfloor {AX} \right\rfloor}{\begin{matrix}\left( {\lbrack X\rbrack_{t} - \lbrack{AX}\rbrack} \right) \\\left( {\lbrack A\rbrack_{t} - \left\lbrack {D_{1}A} \right\rbrack - \left\lbrack {D_{2}A} \right\rbrack - \left\lbrack {D_{3}A} \right\rbrack - \lbrack{AX}\rbrack} \right)\end{matrix}}}} & \text{(Equation~~18)}\end{matrix}$

Analogously, three theta values, which differ by the excitationwavelength, can be defined. $\begin{matrix}{\theta_{n}^{\lambda_{1}} = {\frac{\left\lbrack {AD}_{1} \right\rbrack}{\left\lbrack D_{1} \right\rbrack_{t}} = \frac{I_{D_{1}}^{\lambda_{1}} - I_{n}^{\lambda_{1}}}{I_{D_{1}}^{\lambda_{1}} - I_{{AD}_{1}}^{\lambda_{1}}}}} & \left( {{Equation}\quad 19A} \right) \\{\theta_{n}^{\lambda_{2}} = {\frac{\left\lbrack {AD}_{2} \right\rbrack}{\left\lbrack D_{2} \right\rbrack_{t}} = \frac{I_{D_{2}}^{\lambda_{2}} - I_{n}^{\lambda_{3}}}{I_{D_{2}}^{\lambda_{2}} - I_{{AD}_{2}}^{\lambda_{2}}}}} & \text{(Equation~~19B)} \\{\theta_{n}^{\lambda_{3}} = {\frac{\left\lbrack {A_{3}D_{3}} \right\rbrack}{\left\lbrack D_{3} \right\rbrack_{t}} = \frac{I_{D_{3}}^{\lambda_{3}} - I_{n}^{\lambda_{3}}}{I_{D_{3}}^{\lambda_{3}} - I_{A_{3}D_{3}}^{\lambda_{3}}}}} & \text{(Equation~~19C)}\end{matrix}$

and thus

[AD ₁]=θ_(n) ^(λ) ^(₁) [D ₃] _(t)   (Equation 20A)

[AD ₂]=θ_(n) ^(λ) ^(₂) [D ₂] _(t)   (Equation 20B)

[AD ₃]=θ_(n) ^(λ) ^(₃) [D ₁] _(t)   (Equation 20C)

Combining equations 20 with equations 17 and 18 and knowledge of thethree K_(AD) values, allows for fitting for the value of K_(AX). Inprinciple, not all K_(AD) values need be known. In this case, theincreased number of unknowns complicates the analysis significantly.

An alternate model, in which AD₁, AD₂ and AD₃ are in equilibrium withXD₁, XD₂ and XD₃ can be derived analogously. Fitting here is morecomplex as the number of unknowns is larger—including

K _(AD) ₂

K _(AD) ₁

K _(AD) ₃

A treatment in which a single donor and multiple acceptors can be usedwhen fluorescence energy transfer can be observed directly (whenacceptor emission is observable) and the acceptor emission spectra donot overlap significantly. Derivation of appropriate equations for thiscase is straightforward and analogous to those derived for the abovecase.

Multiple Acceptor/Multiple Donor Methods

Several donor acceptor/complexes can be monitored in solutionsimultaneously. Each donor must have a unique excitation wavelength andeach acceptor an absorbance spectrum corresponding to the emission ofits donor. If emission of the acceptor is to be monitored, the emissionspectra of the acceptors must be unique. Some correction for overlap canbe made; however, such necessity complicates the data analysissignificantly. The number of donor acceptor pairs is, in principle,unlimited.

Multiple donor acceptor pairs are designated A₁D₁, A₂D₂, A₃D₃, etc. Anexample is provided using three AD pairs, but any number is possible.Equations accounting for the multiple simultaneous equilibria aredescribed below. $\begin{matrix}{K_{A_{1}D_{1}} = {\frac{\left\lfloor {A_{3}D_{2}} \right\rfloor}{{\left\lbrack D_{1} \right\rbrack_{f}\left\lbrack A_{1} \right\rbrack}_{f}} = \frac{\left\lfloor {A_{1}D_{1}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{1} \right\rbrack_{t} - \left\lbrack {A_{1}D_{1}} \right\rbrack - \left\lbrack {A_{2}D_{1}} \right\rbrack - \left\lbrack {A_{3}D_{1}} \right\rbrack} \right) \\\left( {\left\lbrack A_{1} \right\rbrack_{t} - \left\lbrack {A_{1}D_{1}} \right\rbrack - \left\lbrack {A_{1}D_{2}} \right\rbrack - \left\lbrack {A_{1}D_{3}} \right\rbrack - \left\lbrack {A_{1}X} \right\rbrack} \right)\end{matrix}}}} & \text{(Equation~~21A)} \\{K_{A_{2}D_{2}} = {\frac{\left\lfloor {A_{2}D_{2}} \right\rfloor}{{\left\lbrack D_{2} \right\rbrack_{f}\left\lbrack A_{2} \right\rbrack}_{f}} = \frac{\left\lfloor {A_{2}D_{2}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2} \right\rbrack_{t} - \left\lbrack {A_{1}D_{2}} \right\rbrack - \left\lbrack {A_{2}D_{2}} \right\rbrack - \left\lbrack {A_{3}D_{2}} \right\rbrack} \right) \\\left( {\left\lbrack A_{2} \right\rbrack_{t} - \left\lbrack {A_{2}D_{1}} \right\rbrack - \left\lbrack {A_{2}D_{2}} \right\rbrack - \left\lbrack {A_{2}D_{3}} \right\rbrack - \left\lbrack {A_{2}X} \right\rbrack} \right)\end{matrix}}}} & \text{(Equation~~21B)} \\{K_{A_{3}D_{2}} = {\frac{\left\lfloor {A_{3}D_{3}} \right\rfloor}{{\left\lbrack D_{3} \right\rbrack_{f}\left\lbrack A_{3} \right\rbrack}_{f}} = \frac{\left\lfloor {A_{3}D_{3}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{3} \right\rbrack_{t} - \left\lbrack {A_{1}D_{3}} \right\rbrack - \left\lbrack {A_{2}D_{3}} \right\rbrack - \left\lbrack {A_{3}D_{3}} \right\rbrack} \right) \\\left( {\left\lbrack A_{3} \right\rbrack_{t} - \left\lbrack {A_{3}D_{1}} \right\rbrack - \left\lbrack {A_{3}D_{2}} \right\rbrack - \left\lbrack {A_{3}D_{3}} \right\rbrack - \left\lbrack {A_{3}X} \right\rbrack} \right)\end{matrix}}}} & \text{(Equation~~21C)} \\{K_{A_{1}X} = {\frac{\left\lfloor {A_{1}X} \right\rfloor}{{\lbrack X\rbrack_{f}\left\lbrack A_{1} \right\rbrack}_{f}} = \frac{\left\lfloor {A_{1}X} \right\rfloor}{\begin{matrix}\left( {\lbrack X\rbrack_{t} - \left\lbrack {A_{1}X} \right\rbrack - \left\lbrack {A_{2}X} \right\rbrack - \left\lbrack {A_{3}X} \right\rbrack} \right) \\\left( {\left\lbrack A_{1} \right\rbrack_{t} - \left\lbrack {A_{1}D_{1}} \right\rbrack - \left\lbrack {A_{1}D_{2}} \right\rbrack - \left\lbrack {A_{1}D_{3}} \right\rbrack - \left\lbrack {A_{1}X} \right\rbrack} \right)\end{matrix}}}} & \text{(Equation~~22)}\end{matrix}$

It is assumed that each X sequence will bind to A₁, A₂, and A₃ withequal affinity, since the three acceptor oligonucleotides have identicalsequences. Therefore, [XA₁]=[XA₂]=[XA₃] and

K _(A) ₁ _(D) =K _(A) ₂ _(D) =K _(A) ₃ _(D)  (Equation 23)

Similar reasoning leads to the assertion that [D₁A₁]=[D₁A₂]=[D₁A₃] andso forth for the other donor sequences. Defining expressions for θ andsubstituting the following expressions for the equilibrium constants itis found that: $\begin{matrix}{\theta_{n}^{\lambda_{1}} = {\frac{\left\lbrack {A_{1}D_{1}} \right\rbrack}{\left\lbrack D_{1} \right\rbrack_{t}} = \frac{I_{D_{I}}^{\lambda_{1}} - I_{n}^{\lambda_{1}}}{I_{D_{I}}^{\lambda_{1}} - I_{A_{1}D_{1}}^{\lambda_{1}}}}} & \left( {{Equation}\quad 24A} \right) \\{\theta_{n}^{\lambda_{2}} = {\frac{\left\lbrack {A_{2}D_{2}} \right\rbrack}{\left\lbrack D_{2} \right\rbrack_{t}} = \frac{I_{D_{2}}^{\lambda_{2}} - I_{n}^{\lambda_{2}}}{I_{D_{2}}^{\lambda_{2}} - I_{A_{2}D_{2}}^{\lambda_{2}}}}} & \text{(Equation~~24B)} \\{\theta_{n}^{\lambda_{3}} = {\frac{\left\lbrack {A_{3}D_{3}} \right\rbrack}{\left\lbrack D_{3} \right\rbrack_{t}} = \frac{I_{D_{3}}^{\lambda_{3}} - I_{n}^{\lambda_{3}}}{I_{D_{3}}^{\lambda_{3}} - I_{A_{3}D_{3}}^{\lambda_{3}}}}} & \text{(Equation~~24C)}\end{matrix}$

Therefore,

θ_(n) ^(λ) ^(₁) [D ₁] _(t) =[A ₁ D ₁ ]=[A ₂ D ₁ ]=[A ₃ D ₁]  (Equation25A)

θ_(n) ^(λ) ^(₂) [D ₂] _(t) =[A ₁ D ₂ ]=[A ₂ D ₂ ]=[A ₃ D ₂]  (Equation25B)

θ_(n) ^(λ) ^(₃) [D ₃] _(t) =[A ₁ D ₃ ]=[A ₂ D ₃ ]=[A ₃ D ₃]  (Equation25C)

Further assume that [D₁]_(t)=[D₂]_(t)=[D₃ _(t)], which is determined bythe experimental setup. $\begin{matrix}{K_{A_{1}D_{1}} = {\frac{\left\lfloor {A_{1}D_{1}} \right\rfloor}{{\left\lbrack D_{1} \right\rbrack_{t}\left\lbrack A_{1} \right\rbrack}_{t}} = \frac{\theta^{\lambda_{1}}}{\begin{matrix}\left( {1 - {3\theta^{\lambda_{1}}}} \right) \\\left( {\left\lbrack A_{1} \right\rbrack_{t} - {\left( {\theta^{\lambda_{1}} + \theta^{\lambda_{2}} + \theta^{\lambda_{3}}} \right)\left\lbrack D_{1} \right\rbrack}_{t} - \left\lbrack {A_{1}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 26A} \right) \\{K_{A_{2}D_{2}} = {\frac{\left\lfloor {A_{2}D_{2}} \right\rfloor}{{\left\lbrack D_{2} \right\rbrack_{t}\left\lbrack A_{2} \right\rbrack}_{t}} = \frac{\theta^{\lambda_{2}}}{\begin{matrix}\left( {1 - {3\theta^{\lambda_{2}}}} \right) \\\left( {\left\lbrack A_{2} \right\rbrack_{t} - {\left( {\theta^{\lambda_{1}} + \theta^{\lambda_{2}} + \theta^{\lambda_{3}}} \right)\left\lbrack D_{2} \right\rbrack}_{t} - \left\lbrack {A_{2}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 26B} \right) \\{K_{A_{3}D_{3}} = {\frac{\left\lfloor {A_{3}D_{3}} \right\rfloor}{{\left\lbrack D_{3} \right\rbrack_{t}\left\lbrack A_{3} \right\rbrack}_{t}} = \frac{\theta^{\lambda_{3}}}{\begin{matrix}\left( {1 - {3\theta^{\lambda_{3}}}} \right) \\\left( {\left\lbrack A_{1} \right\rbrack_{t} - {\left( {\theta^{\lambda_{1}} + \theta^{\lambda_{2}} + \theta^{\lambda_{3}}} \right)\left\lbrack D_{3} \right\rbrack}_{t} - \left\lbrack {A_{3}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 26C} \right) \\{K_{A_{1}X} = {\frac{\left\lfloor {A_{1}X} \right\rfloor}{{\lbrack X\rbrack_{t}\left\lbrack A_{1} \right\rbrack}_{t}} = \frac{\left\lfloor {A_{1}X} \right\rfloor}{\begin{matrix}\left( {\lbrack X\rbrack_{t} - {3\left\lbrack {A_{1}X} \right\rbrack}} \right) \\\left( {\left\lbrack A_{1} \right\rbrack_{t} - {\left( {\theta^{\lambda_{1}} + \theta^{\lambda_{2}} + \theta^{\lambda_{3}}} \right)\left\lbrack D_{1} \right\rbrack}_{t} - \left\lbrack {A_{1}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 27} \right)\end{matrix}$

Equations for

K _(A) ₂ _(D)

and

K _(A) ₃ _(D)

assume similar forms and as noted above are assumed equal to

K _(A) ₁ _(D)

This system of equations (Equations 26 & 27) must be solved by iterativemethods to find a value of K_(AX) which satisfies, at each X_(t), theconstraints imposed by the known concentrations of the AD complexesderived from the measured θ values.

A fundamentally different strategy for simultaneous monitoring ofmultiple donor/acceptor pairs is to use the dyes as acceptor and donor,but on different duplexes. Again, discrimination is made optically.Here, an example is provided using three donor/acceptor complexes, butthe method is not limited in the number of complexes that can beemployed.

The nomenclature is altered slightly from that used above. Here, eachfluorescent dye is designated as D, with superscript A indicating thatdye D is acting as an acceptor and superscript D indicating that dye Dis acting as a donor. Dyes are attached to oligonucleotides such thatthree FET-capable duplexes can form: D^(A) ₂D^(D) ₁, D^(A) ₃D^(D) ₂, andD^(A) ₄D^(D) ₃. Dye D₁ acts only as a donor and D₄ only as an acceptor;however, dyes D₂ and D₃ act as acceptor and donor, but on differentduplexes. Again, the oligonucleotides are designed so that D^(A) ₂D^(D)₁, D^(A) ₃D^(D) ₂, and D^(A) ₄D^(D) ₃ vary in stability systematicallyand so that the X strand can form duplexes with the acceptor bearingstrands, namely D^(A) ₂X, D^(A) ₃X and D^(A) ₄X.

As in the cases described above, equilibrium constants can be derivedrelating the concentrations of the various solution components.$\begin{matrix}{K_{D_{1}^{A}D_{1}^{D}} = {\frac{\left\lfloor {D_{2}^{A}D_{1}^{D}} \right\rfloor}{{\left\lbrack D_{1}^{D} \right\rbrack_{f}\left\lbrack D_{2}^{A} \right\rbrack}_{f}} = \frac{\left\lfloor {D_{2}^{A}D_{1}^{D}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{1}^{D} \right\rbrack_{t} - \left\lbrack {D_{2}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{1}^{D}} \right\rbrack} \right) \\\left( {\left\lbrack D_{2}^{A} \right\rbrack_{t} - \left\lbrack {D_{2}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 28A} \right) \\{K_{D_{1}^{A}D_{2}^{D}} = {\frac{\left\lfloor {D_{3}^{A}D_{2}^{D}} \right\rfloor}{{\left\lbrack D_{2}^{D} \right\rbrack_{f}\left\lbrack D_{3}^{A} \right\rbrack}_{f}} = \frac{\left\lfloor {D_{3}^{A}D_{2}^{D}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2}^{D} \right\rbrack_{t} - \left\lbrack {D_{2}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{2}^{D}} \right\rbrack} \right) \\\left( {\left\lbrack D_{3}^{A} \right\rbrack_{t} - \left\lbrack {D_{3}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 28B} \right) \\{K_{D_{1}^{A}D_{3}^{D}} = {\frac{\left\lfloor {D_{4}^{A}D_{3}^{D}} \right\rfloor}{{\left\lbrack D_{3}^{D} \right\rbrack_{f}\left\lbrack D_{4}^{A} \right\rbrack}_{f}} = \frac{\left\lfloor {D_{4}^{A}D_{3}^{D}} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{3}^{D} \right\rbrack_{t} - \left\lbrack {D_{2}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{3}^{D}} \right\rbrack} \right) \\\left( {\left\lbrack D_{4}^{A} \right\rbrack_{t} - \left\lbrack {D_{4}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 28C} \right)\end{matrix}$

Because the acceptor strands are not identical (the dyes differ althoughthe oligonucleotides to which they are attached are identical), thereare three additional equilibrium constants to define. $\begin{matrix}{K_{D_{2}^{A}X} = {\frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{{\left\lbrack D_{1}^{A} \right\rbrack_{f}\lbrack X\rbrack}_{f}} = \frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2}^{A} \right\rbrack_{t} - \left\lbrack {D_{2}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{2}^{A}X} \right\rbrack} \right) \\\left( {\lbrack X\rbrack_{t} - \left\lbrack {D_{2}^{A}X} \right\rbrack - \left\lbrack {D_{3}^{A}X} \right\rbrack - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 29A} \right) \\{K_{D_{3}^{A}X} = {\frac{\left\lfloor {D_{3}^{A}X} \right\rfloor}{{\left\lbrack D_{2}^{A} \right\rbrack_{f}\lbrack X\rbrack}_{f}} = \frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2}^{A} \right\rbrack_{t} - \left\lbrack {D_{3}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{3}^{A}X} \right\rbrack} \right) \\\left( {\lbrack X\rbrack_{t} - \left\lbrack {D_{2}^{A}X} \right\rbrack - \left\lbrack {D_{3}^{A}X} \right\rbrack - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 29B} \right) \\{K_{D_{4}^{A}X} = {\frac{\left\lfloor {D_{4}^{A}X} \right\rfloor}{{\left\lbrack D_{4}^{A} \right\rbrack_{f}\lbrack X\rbrack}_{f}} = \frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{4}^{A} \right\rbrack_{t} - \left\lbrack {D_{4}^{A}D_{1}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{2}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}D_{3}^{D}} \right\rbrack - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right) \\\left( {\lbrack X\rbrack_{t} - \left\lbrack {D_{2}^{A}X} \right\rbrack - \left\lbrack {D_{3}^{A}X} \right\rbrack - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right)\end{matrix}}}} & \left( {{Equation}\quad 29C} \right)\end{matrix}$

If the dyes do not perturb the equilibria significantly, it isreasonable to assume that K_(D) ₂ _(^(A)) _(X)=K_(D) ₃ _(^(A))_(X)=K_(D) ₄ _(^(A)) _(X). The assumption that the acceptor dyes areequally perturbing or non-perturbing is reasonable and testable.$\begin{matrix}{\quad {\theta_{n}^{\lambda_{2}} = {\frac{\left\lbrack {D_{2}^{A}D_{1}^{D}} \right\rbrack}{\left\lbrack D_{1}^{D} \right\rbrack_{t}} = \frac{I_{D_{1}^{D}}^{\lambda_{1}} - I_{n}^{\lambda_{1}}}{I_{D_{1}^{D}}^{\lambda_{1}} - I_{D_{2}^{A}D_{1}^{D}}^{\lambda_{1}}}}}} & \left( {{Equation}\quad 30A} \right) \\{\theta_{n}^{\lambda_{2}} = {\frac{\left\lbrack {D_{1}^{A}D_{2}^{D}} \right\rbrack}{\left\lbrack D_{2}^{D} \right\rbrack_{t}} = {\frac{\left( {I_{D_{2}^{D}}^{\lambda_{2}} + I_{D_{2}^{A}}^{\lambda_{2}}} \right) - \left( {I_{n}^{\lambda_{2}} + I_{D_{2}^{A}}^{\lambda_{2}}} \right)}{\left( {I_{D_{2}^{D}}^{\lambda_{2}} + I_{D_{2}^{A}}^{\lambda_{2}}} \right) - \left( {I_{D_{3}^{A}D_{2}^{D}}^{\lambda_{2}} + I_{D_{2}^{A}}^{\lambda_{2}}} \right)} = \frac{I_{D_{2}^{D}}^{\lambda_{2}} - I_{n}^{\lambda_{2}}}{I_{D_{2}^{D}}^{\lambda_{2}} - I_{D_{3}^{A}D_{2}^{D}}^{\lambda_{2}}}}}} & \left( {{Equation}\quad 30B} \right) \\{\theta_{n}^{\lambda_{3}} = {\frac{\left\lbrack {D_{4}^{A}D_{3}^{D}} \right\rbrack}{\left\lbrack D_{3}^{D} \right\rbrack_{t}} = {\frac{\left( {I_{D_{3}^{D}}^{\lambda_{3}} + I_{D_{3}^{A}}^{\lambda_{3}}} \right) - \left( {I_{n}^{\lambda_{3}} + I_{D_{3}^{A}}^{\lambda_{3}}} \right)}{\left( {I_{D_{3}^{D}}^{\lambda_{3}} + I_{D_{3}^{A}}^{\lambda_{3}}} \right) - \left( {I_{D_{4}^{A}D_{3}^{D}}^{\lambda_{3}} + I_{D_{3}^{A}}^{\lambda_{3}}} \right)} = \frac{I_{D_{3}^{D}}^{\lambda_{3}} - I_{n}^{\lambda_{3}}}{I_{D_{3}^{D}}^{\lambda_{3}} - I_{D_{4}^{A}D_{3}^{D}}^{\lambda_{3}}}}}} & \left( {{Equation}\quad 30C} \right)\end{matrix}$

Note that in the expressions for be and θ_(n) ^(λ) ^(₂) and θ_(n) ^(λ)^(₃) , the measured quantities (shown in parentheses) containcontributions from the fluorescence of the acceptor of the previous (asin the assigned index) donor acceptor pair. This is assumed to beindependent of the formation of the complex. This assumption istestable, should it not be valid appropriate corrections can be applied.

As in the above analyses, the concentrations of the donor/acceptorcomplexes can be determined by measurement of the θ values and knowledgeof the total concentrations of the donor strands.

 └D ₁ ^(A) D ₁ ^(D)┘=θ_(n) ^(λ) ^(₁) └D ₁ ^(D)┘_(t)  (Equation 31A)

└D ₁ ^(A) D ₁ ¹┘=θ_(n) ^(λ) ^(₂) └D ₂ ^(D)┘_(t)  (Equation 31B)

└D ₄ ^(A) D ₁ ^(D)┘=θ_(n) ^(λ) ^(₃) └D ₁ ^(D)┘_(t)  (Equation 31C)

Again substituting values for the θ terms and assuming that [D₁^(D)]_(t)=[D₂ ^(D)]_(t)=[D₁ ^(D)]_(t), which is determined by theexperimental setup, a system of equations is presented that can besolved as a function of [X]_(t) to find values for

K _(D) ₂ _(^(A)) _(A) =K _(D) ₃ _(^(A)) _(A) =K _(D) ₄ _(^(A)) _(A)$\begin{matrix}{K_{D_{2}^{A}D_{1}^{D}} = {\frac{\left\lfloor {D_{2}^{A}D_{1}^{D}} \right\rfloor}{{\left\lbrack D_{1}^{D} \right\rbrack_{f}\left\lbrack D_{2}^{A} \right\rbrack}_{f}} = \frac{\theta_{n}^{\lambda_{1}}}{\left( {1 - {3\theta_{n}^{\lambda_{1}}}} \right)\left( {\left\lbrack D_{2}^{A} \right\rbrack_{t} - {\left( {\theta_{n}^{\lambda_{1}} + \theta_{n}^{\lambda_{2}} + \theta_{n}^{\lambda_{3}}} \right)\left\lbrack D_{1}^{D} \right\rbrack}_{t} - \left\lbrack {D_{2}^{A}X} \right\rbrack} \right)}}} & \left( {{Equation}\quad 32A} \right) \\{K_{D_{3}^{A}D_{2}^{D}} = {\frac{\left\lfloor {D_{2}^{A}D_{2}^{D}} \right\rfloor}{{\left\lbrack D_{2}^{D} \right\rbrack_{f}\left\lbrack D_{3}^{A} \right\rbrack}_{f}} = \frac{\theta_{n}^{\lambda_{2}}}{\left( {1 - {3\theta_{n}^{\lambda_{2}}}} \right)\left( {\left\lbrack D_{3}^{A} \right\rbrack_{t} - {\left( {\theta_{n}^{\lambda_{1}} + \theta_{n}^{\lambda_{2}} + \theta_{n}^{\lambda_{3}}} \right)\left\lbrack D_{2}^{D} \right\rbrack}_{t} - \left\lbrack {D_{3}^{A}X} \right\rbrack} \right)}}} & \left( {{Equation}\quad 32B} \right) \\{K_{D_{4}^{A}D_{3}^{D}} = {\frac{\left\lfloor {D_{4}^{A}D_{3}^{D}} \right\rfloor}{{\left\lbrack D_{3}^{D} \right\rbrack_{f}\left\lbrack D_{4}^{A} \right\rbrack}_{f}} = \frac{\theta_{n}^{\lambda_{3}}}{\left( {1 - {3\theta_{n}^{\lambda_{3}}}} \right)\left( {\left\lbrack D_{4}^{A} \right\rbrack_{t} - {\left( {\theta_{n}^{\lambda_{1}} + \theta_{n}^{\lambda_{2}} + \theta_{n}^{\lambda_{3}}} \right)\left\lbrack D_{3}^{D} \right\rbrack}_{t} - \left\lbrack {D_{4}^{A}X} \right\rbrack} \right)}}} & \left( {{Equation}\quad 32C} \right) \\{K_{D_{2}^{A}X} = {\frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{{\left\lbrack D_{2}^{D} \right\rbrack_{f}\lbrack X\rbrack}_{f}} = \frac{\left\lfloor {D_{2}^{A}X} \right\rfloor}{\begin{matrix}\left( {\left\lbrack D_{2}^{A} \right\rbrack_{t} - {\left( {\theta_{n}^{\lambda_{1}} + \theta_{n}^{\lambda_{2}} + \theta_{n}^{\lambda_{3}}} \right)\left\lbrack D_{2}^{A} \right\rbrack}_{t} - \left\lbrack {D_{2}^{A}X} \right\rbrack} \right) \\\left( {\lbrack X\rbrack_{t} - {3\left\lbrack {D_{2}^{A}X} \right\rbrack}} \right)\end{matrix}}}} & \left( {{Equation}\quad 33} \right)\end{matrix}$

Expressions for

K _(D) ₃ _(^(A)) _(A)

and

K _(D) ₄ _(^(A)) _(A)

are derived similarly and, as described above, their values are assumedto be identical to

K _(D) ₂ _(^(A)) _(A)

The advantage of this method of multiple simultaneous titration, wheresome of the dyes act as both donor and acceptor (although on differentoligonucleotides), over the method described above, in which all donorsand acceptors are unique, is that the probability of identification of aset of fluorescent dyes with the necessary photophysical properties isenhanced.

While there are restrictions on the properties of a set of dyes usablein simultaneous titrations, there are likely to be many sets of usabledyes. One such set of dyes is described in the table below. Each of themis available from Molecular Probes, Inc. of Eugene, Oreg.

Donor Acceptor Fluorescent Dye D₁ ^(D) — Alexa 350 D₂ ^(D) D₂ ^(A) Alexa430 D₃ ^(D) D₃ ^(A) Alexa 488 — D₄ ^(A) Alexa 594

When one of the reference duplex strands is attached to a surface, onlythe other strand need be labeled. In this embodiment, the measurement isnot FET, but rather fluorescence. A washing step must be included inthis embodiment to remove released label. However, this modification maydisturb the equilibria rendering this embodiment of the assay morequalitative than quantitative.

Multiple measurements can be conducted simultaneously on a surface. Aseries of different strands can be attached to a surface so as toidentify a particular oligonucleotide with its location on the surface.This kind of spatial distribution of different oligonucleotides is wellknown. The fluorophore can be attached post-synthetically or as aphosphoramidite; either method is compatible with methods for producingan oligonucleotide array on a surface. A single oligonucleotide withsufficient complementarity to form reference duplexes with each of theimmobilized strands can be used to form a series of reference duplexes.The surface is then exposed to a single target that simultaneouslyequilibrates with all of the reference duplexes. A series of standardscan be routinely incorporated into this assay.

The method of the present invention is of particular use in singlenucleotide polymorphism (SNP) screening. The theory behind theapplication of this FET assay to SNP screening is based upon twosegments of DNA, the first being a “wild type” sequence (does notcontain a SNP), and the second being a variant sequence (a SNP) that,for example, may be a marker for disease or disease tendency.Standardized methods abound for amplifying a small genetic sample (e.g.from a few microliters of blood), and the result would be one amplifiedstrand, which would become the unlabeled competitor (X) strand in ourFET assay. When amplification of the target is performed the quantity ofthe target can be determined by use of labeled primers. Eitherfluorescently labeled, so as not to interfered with the subsequent FETmeasurement, or by any of the many well known methods for labelingamplification products.

Since SNP screening is merely a detection of a SNP, and not aquantitation of energetic impact per se, FET-based SNP screening doesnot even require a full titration of target (X) into the donor-acceptorduplex. Merely adding a fixed excess amount of the X strand issufficient, in effect making a two-point titration wherein thefluorescence is measured before and after X addition. The amount of Xstrand needed should be in the range of 10- to 100-fold excess overdonor (D). In these experiments, when the sequences of X and D match, Xwill efficiently displace D from the donor acceptor duplex, causing anefficient, and probably complete, reduction in θ. When X and D do notmatch, θ will remain high. In theory, either experiment would besufficient to prove the presence or absence of wild-type sequence.However, it is generally preferable to guarantee that a positive andnegative signal will be achieved in clinical assays, so it would bepreferable to run two experiments in parallel, monitoring donor-acceptorduplexes of wild-type and SNP sequences, one of which should have high θand one low θ. Additionally, a heterozygous sample would score as anefficient competitor for both donor-acceptor duplexes.

The assay is further applicable to situations where there may bemultiple SNP sites within a single gene, with each variation occurringat low frequency. In this embodiment, a much longer sequence can bescreened similarly, still in a single experiment. In such a case, thedonor-acceptor duplex has the wild-type sequence of the full length ofthe region of interest. The amplified target strand, X, is judged, froma single 10- to 100-fold addition, to either compete or not for thedonor-acceptor duplex. If FET is reduced, and X is a good competitor,then further screening could be done using additional assays morespecific in nature to the sequences in question. Even if anotherspecific screening method is preferred, the global nature of the FETassay is useful as a first screen, eliminating the cost and expense ofscreening by other more detailed methods for every single patient beingtested. If, among all SNPs identified within a gene, the frequency runsas high as 20% for having any one variation, the single screen using avery long sequence would still eliminate the need for extensive testingon 80% of the samples. This would represent a large savings in material,and would greatly improve the throughput of testing facilities.

The SNP assay is not limited by the length of the strands (e.g. numberof bases long) that are being screened. The actual length limitation isa theoretical barrier attributable to a kinetic situation whereby verylong uniquely complementary sequences may not ever form a completeduplex. This limitation is similar to the fact that long sequences suchas complete bacterial genomes cannot be completely reannealed afterthermal disruption. The barrier for this assay is estimated to be in therange of several hundreds of bases, such that sequences of interest inthe range of up to 100 bases can be easily accommodated. Clearly, longersequences, however, are considered within the scope of this assay.

The relevance of a strand length of about 100 bases, however, is thatregions bearing even one SNP may be assessed by a single assay, usingthis method. As SNP identity becomes linked to disease potential inhumans, such screening becomes an extremely valuable technique for rapiddiagnosis of individual patients, both for diagnosis of ailment,infection, drug sensitivity, drug resistance, etc., and early detectionof conditions that can lead to timely application of preventativetreatments. Regions of genes already identified as having relevant SNPsare generally in the range of 100 bases or less, meaning that thetheoretical length limitation will not become a factor in practice.

The key feature of this method that eliminates length of theoligonucleotides as a limitation, unlike in other assays undercommercial development, is that this method depends on competitionbetween two different equilibria characterized by two differentequilibrium constants. Thus the actual measurement is the ratio of thetwo equilibrium constants, and thus the difference in free energies forformation of these alternative duplexes. The difference in free energycaused by a defect, such as a single base pair mismatch (i.e. not acanonical Watson-Crick pairing), is the same whether the defect iswithin a very long duplex or a short one, so long as the bulk of theduplex generally remains stable. Thus, the magnitude of ΔG° is not aconsideration, since the fluorescence assay measures the difference intwo ΔG° values (ΔΔG°) directly. Mismatches of the four canonical baseswill generally exhibit ΔΔG° values of about 1 or 2 kcal/mol, but this 1to 2 kcal/mol is the actual magnitude of the measurement itself. Thus,whether the absolute values are 20 kcal/mol of duplex, as in a 10-15base pair oligonucleotide, or 600 kcal/mol of duplex, in somethingperhaps as long as a gene, the assay is silent to these magnitudes,because it is reporting ΔΔG° directly.

Fluorescently labeled strands used in the present invention may beprovided in a kit form. A researcher interested in adapting their testDNA lesion could do so simply by synthesizing a small amount of test DNAwithin a sequence predefined by the kit DNA. A kit would include atleast one FET-labeled starting duplex and the appropriate buffer alongwith simple instructions for performing the experiment and analyzing thedata. The kit may also include a standardized competitor strand toensure reproducibility and to facilitate comparisons over time. As anexample, the strands of a kit could be designed with specific targets inmind. A specific kit could be designed, for example, to screen for asingle mutation in a gene.

The following nonlimiting examples are provided to further illustratethe present invention.

EXAMPLES Example 1

Purification and Dye-labeling of 5′-amino-linker Oligonucleotides

Standard phosphoramidite DNA synthesis with an amino-linkerphosphoramidite as the last (5′) residue is performed. The intactsynthesis column is dried under vacuum. The column is then cracked openand the glass support beads are transferred to a screw top plasticbottle. Aqueous NH₄OH (1 ml) from the freezer is added to each tube andthe DNA is deprotected for three days at room temperature for standardamidites. Tubes are then cooled in the freezer and the NH₄OH is pipettedoff. The supports are then washed with 2×200 μl water or a mixture ofEtOH:CH₃CN:H₂O (3:1:1); the samples and washes are combined; and thendried in a Speed-Vac. The dried samples are then dissolved in H₂O at lowtemperature (<40° C.) and floating non-soluble materials are removed. Atthis step, the sample may be purified by reverse phase, using highperformance liquid chromatography (HPLC ) and a PRP-column, equilibratedwith 50 mM ammonium bicarbonate. Elution is performed by a linear(5-50%) gradient of acetonitrile in 50 mM NH₄HCO₃. Followingfreeze-drying, the fractions containing the purified tritylatedN-modified oligonucleotide are heated to 95° C. for 5 minutes to removethe MMT-(trityl) group and subjected to ethanol precipitation in thepresence of sodium ions, as follows: the volume is adjusted to 300 to400 μl water; NaCl (100 μl, 2M) or sodium buffer is then added alongwith 950 μl of EtOH; samples are then placed in the freezer for at least30 minutes, preferably one hour. Following freezing, the sample iscentrifuged for 12 minutes at 14,000 rpm. The resulting pellet is driedto remove any residual ethanol. Trityl is then removed by addition of200 μl of 80% acetic acid for one hour at room temperature andevaporating the liquid in a Speed-Vac for 2 to 3 hours until a glassyresidue is observed. This step is critical to ensure elimination of anyresidual free amines that might interfere with the labeling reaction.For the unlabeled oligonucleotides, the trityl group is removed byaddition of 80% acetic acid and incubation for one hour at roomtemperature, followed by freeze drying. Both the purity of the finalproduct and the success of detritylation are monitored by analyticalreverse phase HPLC. If required, additional purification of thedetritylated oligonucleotide is performed by reverse phase HPLC. Thepurified DNA is subjected to ethanol precipitation/Na+ exchange to ridthe sample of any excess reactive amines from the HPLC buffer andlabeled as follows: DNA (30-40 OD-260) is dissolved in 270 μl of H₂O inan O-ring tube. NaHCO₃ (30 μl, 1 M) at pH 8.3 is then added. One mg ofsuccinyl ester form of the dye is then added for each 20 OD of DNA. Thiscan be weighed as a dry reagent into a glass vial, dissolved in 80 μl/mgof fresh DMSO, and added into the plastic tube of DNA solution. Theglass vial is then rinsed with 20 μl of additional DMSO and added to theplastic tube. Alternatively, a 100 μl aliquot of dye is added. The dyeand DNA are then allowed to react at 37° C. or higher at leastovernight.

The DNA is then isolated from any unreacted dye with a PD-10 SephadexG-25 column (Pharmacia). The column is equilibrated by rinsing with atleast 25 ml of H₂O. The DNA sample is diluted with H₂O to a final volumeof 1000 μl and loaded onto the column. The DNA is then washed using 1.6ml H₂O. DNA is eluted in 600 μl fractions with H₂O. Generally sixfractions are sufficient.

The fractions are dried to at least A the volume and adjusted to 300 μltotal volume with H₂O. Each fraction is then independently subjected toethanol precipitation. Generally only the first three fractions willhave appreciable DNA. The free dye stays mostly dissolved in theethanol.

The DNA containing precipitates are combined and the labeled DNApurified using ion exchange HPLC (Mono-Q column) with Buffer A being 50mM Tris HCl with 15% acetonitrile and Buffer B being Buffer A with 1 MNaCl. The gradient profile can be tailored but in general increases from0 to 80% buffer B over 25-35 minutes. Monitoring absorbance at both 260nm and the absorbance maximum of the attached fluorophore can help todefine the labeled and unlabeled DNA peaks.

The labeled DNA is further purified by HPLC using an ion exchange column(e.g. Mono Q, Pharmacia) equilibrated with 50 mM Tris HCl and 15%acetonitrile (Buffer A) and a linear gradient (0-100%) of Buffer B(i.e., Buffer A containing 1 M NaCl). Absorbances at 260 nm and thewavelength corresponding to the maximum absorbance of the fluorophoreare use to monitor and define labeled and unlabeled pools ofoligonucleotides.

Alternatively, a desalting column can be used in place of the ethanolprecipitation steps.

5-labeled oligonucleotides forming duplexes have been compared with theparent unlabeled duplexes, revealing no alterations in theirthermodynamic stability in the presence of the probes. Moreover, theability to form Watson-Crick duplexes in a stoichiometric ratio has beenfurther confirmed by HPLC analysis of the annealed mixtures, incomparison to the free oligonucleotide strands. Additional evidencereveals that both labeled and unlabeled oligonucleotides may berecovered upon completion of a FET assay by repurification, with noindication of adulteration. Time-dependent studies of the integrity ofthe labeled oligonucleotides reveal no sign of aggregation ordegradation within 1 year from sample preparation. The labeledoligonucleotides may be stored as stock solutions in water and workingbuffer at or below −20° C. for at least six months. Preferably, thesamples should be stored as a lyophilized powder, for periods exceedingsix months.

Example 2

Determination of Labeled DNA Concentration

Determination of the concentration of the labeled DNA strands in stocksolutions has been performed using an average extinction coefficient of1.1×10⁵ M⁻¹cm⁻¹ at 25° C. The intrinsic DNA absorbance at 260 nm hasbeen demonstrated to not be significantly altered by the presence of theconjugated dye.

Example 3

Formation of the FET Duplex

A working stock solution of each of the labeled DNA of complementarysequence in the range of 2 to 3 micromole DNA strand is prepared.Fluorescence detection is performed as follows: after each aliquot (ofany titrant) the cuvette is heated to about 90° C., using an externalheat block, and cooled to 25° C. via the intrinsic cooling of thejacketed cuvette holder in the fluorometer. The cuvette must be tightlystoppered to minimize evaporation during heating. Wavelengths must betailored for the dyes used. For example, for the fluorophore pair OregonGreen 514 and Rhodamine-Red-X, the emission spectrum is collected over510-650 nm with excitation at 508 nm, with scanning at 100 nm perminute. The time drive is set to collect, using the kinetics mode, 30 or60 seconds (at 0.1 second per reading) using 508 nm excitation and 528nm emission. These data points are then averaged, resulting in a preciserelative fluorescence intensity for each reading, and an associatedstandard deviation for that averaged value. The fluorescence of thebuffer alone is read to establish a blank for the instrument response.

The fluorescence of the “free” donor strand is then determined. A sampleof 10 nM donor strand is prepared in 250 μl total volume of buffer andfluorescence is measured. An aliquot of the acceptor strand from theworking stock sufficient to achieve a final concentration of 100 nM isthen added to form the FET duplex and the fluorescence is determined.

Example 4

Titration of the Competing Strand

A working stock of the competing strand is prepared at a concentrationappropriate to the expected ability/inability to compete for duplexformation with the formed donor/acceptor pair. In general, theconcentration is one order of magnitude higher than the donor andacceptor working stocks for each 1 kcal/mol of free energy difference(ΔΔG) expected for the competing strand. In the event the free energydifferences are completely unknown, a number of concentrations can beprepared, covering a wide range of concentrations, i.e., 2 μM, 20 μM,200 μM, etc. solutions in buffer. Titration is started with the mostdilute solution and more concentrated solutions are used as necessary.

For the first aliquot, the competing strand is added to a finalconcentration of about ½ of the concentration of the donor/acceptorconcentration. The fluorescence is then determined. If there is asignificant change in the fluorescence, titration is continued with theworking stock. It there is no change, titration is continued with ahigher working stock concentration. Additional aliquots are added andthe fluorescence determined until the fluorescence intensity recovers toat least ½ of the intensity measured for the free donor strand.

Example 5

Automation of Competitive Titration Experiment

The FET data acquisition protocol was automated on an AVIV Model ATF-105Automatic Titrating Fluorescence Spectrophotometer. The customizedsoftware developed for the FET assay on this particular instrumentimproved the overall accuracy, precision, and data throughput comparedto conventional manual titration experiments. There are several keyfeatures of the automated FET assay including programmed titration ofacceptor and competitor or target strands and the ability to conductsuccessive heating/cooling cycles of the sample solution in the cuvette.Selection of the upper temperature limit is dictated by two importantconsiderations, is namely that the parent and test duplexes aredissociated into single strands and the covalently attached fluorophoresare stable at the desired upper temperature. Extensive control studiesconducted on the stability of the Oregon Green 514 (OG) andRhodamine-Red-X (RdRX) labeled strands indicate that these fluorophoresretain their integrity during successive heating/cooling cycles over thetemperature range of 0-75°. The superimposition of UV melting/coolingcurves reveled that the fluorescently labeled strands in the parentduplex are not labile below 75° C. The overall reproducibility iscompromised when heating the identical duplex to temperatures above 75°C., as noted in the family of non-superimposable UV melting/coolingcurves. It is incumbent upon the analyst to judiciously evaluate andselect the practical upper temperature limit for a particular duplex andset of fluorophores.

A typical experiment is initiated by placing a cuvette containing a 100nM solution of the Oregon Green 514 labeled donor strand in the samplecompartment, heating the cuvette to 75° C., maintaining the temperatureat 75° C. for three minutes, and cooling the sample to 20° C. over anequilibration period of five minutes. During the cooling cycle, theinstrument is operated in the kinetic mode and the fluorescence emissionintensity is recorded at 521 nm (i.e. excitation wavelength=508 nm) atfive second intervals. After the fluorescence intensity plateausindicating that equilibrium is achieved, a reference spectrum of thedonor strand is recorded over the wavelength range of 510-650 nm.Activation of the first syringe drive dispenses fixed microliteraliquots of the Rhodamine-Red-X labeled acceptor strand in the samplecuvette to form the FET-active donor-acceptor reference duplex. Uponaddition of each aliquot of acceptor, the sample is subjected to aheating/cooling cycle identical to that above to ensure that the duplexanneals properly. The donor strand (D) d(GCGTACACATGCG)-OG (SEQ ID NO:1)is titrated with its complementary acceptor strand (A)d(CGCATGTGTACGC)-RdRX (SEQ ID NO;2) to form the FET-active referencedonor-acceptor duplex. The diluted corrected fluorescence intensitiesare cast in the form of a Job Plot to confirm that the stoichiometry ofthe single strands in the reference duplex is 1:1 (i.e. molefraction=0.5). Although the forward titration demonstrates that thesingle strands associate to form a competent duplex, the experimentalprotocol may be simplified by loading the pre-formed reference duplexinto the cuvette prior to conducting the automated competitionexperiment. Elimination of the forward titration increases the samplethroughput by reducing overall experimental time in the FET assay byapproximately 50 percent.

Having formed the FET active reference duplex in the initial part of theexperiment, the second syringe drive is activated to dispense fixedaliquots of the unlabeled competing strand (X)d(CGCATGFGTACGC)(SEQ IDNO:3). The sample solution containing the three strands is subjected toheating/cooling cycles after each addition in the titration experimentto facilitate annealing of the donor-acceptor and acceptor-target (AX)duplexes. A sufficient excess of the target strand X (in this caseapproximately 100 fold) is titrated into the cuvette to ensure that atleast half of the acceptor has been displaced from the reference duplex.The dilution corrected relative fluorescence (θ) is plotted as afunction of the concentrations of acceptor (A) and target (X) strands.The concentration of competing strand (X_(0.5)) at which exactly half ofthe acceptor/donor duplex (AD) is disrupted, that is θ=0.5, isinterpolated from this plot. Substituting the value for X_(0.5) into thesimplified relation:

K _(AX)=(K _(AD) ·D _(t)/2·X _(0.5))

yields a value for the acceptor/target association constant (K_(AX)).Application of the thermodynamic relation between ΔG° and K_(AX)facilitates calculation of the free energy:

ΔG°=−R·T·ln K _(AX)

In this example, values of X_(0.5)=1.1×10⁻⁵ for d(CGCATGFGTACGC)(SEQ IDNO:3) and D_(t)=4.22×10⁻⁸ for d(GCGTACACATGCG)-OG (SEQ ID NO:1), coupledwith a K_(AD)=9.0×10¹⁴ determined independently for the referenceduplex, results in a K_(AX)=1.7×10¹² for the formation of the AX duplex.Substitution into the relevant relation yields a value of ΔG°=16.4kcal/mol for the AX duplex that compares favorably with the valuedetermined previously (i.e. ΔG°=16.0 kcal/mol) employing a combinationof calorimetric and spectroscopic technique.

Example 6

Equation Programs

Equation 6 Program

‘declare globals’

Dim At, Dt, Xt, Kad, Kax As Double

Function theta(z1, z2, z3, z4, z5) As Double

At=z1

Dt=z2

Kad=z3

Kax=z4

Xt=z5

theta=ModRegFal(0#, 1#)

End Function

Private Function func1(A) As Double

func1=At*(1−A)/((1+Xt*Kax)/Kad+Dt*(1−A)−A

End Function

Private Function ModRegFal(X1, X2 As Double) As Double

‘Modified Regula Falsi’

‘(adapted from Conte & de Boor, 1980)’

‘Finds root of function func1, if bracketed’

Const xtol=0.000000000001

Const ftol=0.000000000000001

Const ntol=100

Dim SignF1, n, PrvsF3 As Integer

Dim F1, F2, F3, X3 As Double

F1=func1(X1)

F2=func1(X2)

‘test whether root is bracketed’

If Sgn(F1)*F2>=0 Then

Debug.Print “X1=”, X1, “X2=”, X2

Debug.Print “func1(X1)=”, F1, “func1(X2)=”, F2

End

End If

X3=X1

F3=F1

‘BEGIN ITERATION’

For n=1 To ntol

‘TEST FOR CONVERGENCE’

‘Is interval small enough?’

If Abs(X1−X2)<=xtol Then

ModRegFal=X3

Exit Function

End If

‘Is F3 small enough?’

If Abs(F3)<=ftol Then

ModRegFal=X3

Exit Function

End If

‘GET NEW GUESS BY LINEAR INTERPOLATION’

X3=(F1*X2−F2*X1)/(F1−F2)

PrvsF3=Sgn(F3)

F3=func1(X3)

‘CHANGE TO NEW INTERVAL’

If Sgn(F1)*F3>=0 Then

X1=X3

F1=F3

If F3*PrvsF3>=0 Then F2=F2/2#

Else

X2=X3

F2=F3

If F3*PrvsF3>=0 Then F1=F1/2#

End If

Next n

‘END ITERATION’

Debug.Print “X1=”, X1, “X2=”, X2, “X3=”, X3

Debug.Print “func1(X1)=”, F1, “func1(X2)=”, F2, “func1(X3)=”, F3

Debug.Print ntol, “iterations without convergence”

End Function

Equation 13 Program

‘declare globals’

Dim At As Double, Dt As Double, Xt As Double

Dim XA As Double, Kad As Double, Kax As Double

Dim AX As Double

Function theta(z1#, z2#, z3#, z4#, z5#) As Double

At=z1

Dt=z2

Kad=z3

Kax=z4

Xt=z5

dummy=ModRegFal2(0#, z1) switch to At

theta=Theta0( )

Debug.Print “AX/Xt=”; AX/Xt; “Theta=”; theta

End Function

Private Function Theta0( ) As Double

Theta0=ModRegFal1(0#, 1#)

End Function

Private Function funcl(A As Double) As Double

funcl=At*(1−A)/((1+(Xt−AX)*Kax)/Kad+Dt*(1−A))−A

End Function

Private Function func2(B As Double) As Double

Dim T0 As Double

AX=B

T0=Theta0( )

func2=At−AX−T0/(Kad*(1−T0))−T0*Dt

End Function

Private Function ModRegFal1(X1 As Double, X2 As Double) As Double

‘Modified Regula Falsi’

‘(adapted from Conte & de Boor, 1980)’

‘Finds root of function func1, if bracketed’

Const xtol=0.000000000001

Const ftol=0.000000000000001

Const ntol=100

Dim SignF1 As Integer, n As Integer, PrvsF3 As Integer

Dim F1 As Double, F2 As Double, F3 As Double, X3 As Double

F1=func1(X1)

F2=func1(X2)

‘test whether root is bracketed’

If Sgn(F1)*F2>0 Then

Debug.Print “root not bracketed”

Debug.Print “X1=”, X1, “X2=”, X2

Debug.Print “func1(X1)=”, F1, “func1(X2)=”, F2

End

End If

X3=X1

F3=F1

‘BEGIN ITERATION’

For n=1 To ntol

‘TEST FOR CONVERGENCE’

‘Is interval small enough?’

If Abs(X1−X2)<=xotl Then

ModRegFal1=X3

Exit Function

End if

‘Is F3 small enough?’

If Abs(F3)<=ftol Then

ModRegFal1=X3

Exit Function

End If

‘GET NEW GUESS BY LINEAR INTERPOLATION’

X3=(F1*X2−F2* X1)/(F1−F2)

PrvsF3=Sgn(F3)

F3=func1(X3)

‘CHANGE TO NEW INTERVAL’

If Sgn(F1)*F3>=0 Then

X1=X3

F1=F3

If F3*PrvsF3>=0 Then F2=F2/2#

Else

X2=X3

F2=F3

If F3*PrvsF3>=0 Then F1=/2#

End If

Next n

‘END ITERATION’

Debug.Print “X1=”, X1, “X2=”, X2, “X3=”, X3

Debug.Print “func1(X1)=”, F1, “func1(X2)=”, F2, “func1(X3)=”, F3

Debug.Print ntol, “iterations without convergence”

End Function

Private Function ModRegFal2(Y1 As Double, Y2 As Double) As Double

‘Modified Regula Falsi’

‘(adapted from Conte & de Boor, 1980)’

‘Finds root of function func2, if bracketed’

Const xtol=0.000000000001

Const ftol=0.0000000001

Const ntol=100

Dim SignF1 As Integer, n As Integer, PrvsF3 As Integer

Dim F1 As Double, F2 As Double, F3 As Double, Y3 As Double

F1=func2(Y1)

F2=func2(Y2)

‘test whether root is bracketed’

If Sgn(F1)*F2>0 Then

Debug.Print “Y1=”, Y1, “Y2=”, Y2

Debug.Print “func2(Y1)=”, F1, “func2(Y2)=”, F2

End

End If

Y3=Y1

F3=F1

‘BEGIN ITERATION’

For n=1 To ntol

‘TEST FOR CONVERGENCE’

‘Is interval small enough?’

If Abs(Y1−Y2)<=xtol Then

ModRegFal2=Y3

Exit Function

End If

‘Is F3 small enough?’

If Abs(F3)<=ftol Then

ModRegFal2=Y3

Exit Function

End If

‘GET NEW GUESS BY LINEAR INTERPOLATION’

Y3=(F1*Y2−F2*Y1)/(F1−F2)

PrvsF3=Sgn(F3)

F3=func2(Y3)

‘CHANGE TO NEW INTERVAL’

If Sgn(F1)*F3>=0 Then

Y1=Y3

F1=F3

If F3*PrvsF3>=0 Then F2=F2/2#

Else

Y2=Y3

F2=F3

If F3*PrvsF3>=0 Then F1=F1/2#

End If

Next n

‘END ITERATION’

Debug.Print “Y1=”, Y1, “Y2=”,Y2, “Y3=”, Y3

Debug.Print “func2(Y1)=”, F1, “func2(Y2)=”, F2, “func2(Y3)=”, F3

Debug.Print ntol, “iterations without convergence”

End Function

3 1 13 DNA Artificial Sequence Description of Artificial SequenceSynthetic 1 gcgtacacat gcg 13 2 13 DNA Artificial Sequence Descriptionof Artificial Sequence Synthetic 2 cgcatgtgta cgc 13 3 13 DNA ArtificialSequence Description of Artificial Sequence Synthetic 3 cgcatgngta cgc13

What is claimed is:
 1. A method for screening for nucleic acid duplexstability by competitive equilibria comprising: (a) producing a solutioncontaining a known amount of an initial nucleic acid duplex with a knownstability, said initial nucleic acid duplex comprising a first nucleicacid strand having a sequence wholly or in part homologous to a targetstrand and labeled with a donor of a FET pair and a second nucleic acidstrand having a sequence wholly or in part complementary to the targetstrand and labeled with an acceptor of the FET pair; (b) titrating thesolution with a second solution comprising a known concentration of thetarget nucleic acid strand which competes with the first nucleic acidstrand of the initial nucleic acid duplex of step (a) for binding to thesecond nucleic acid strand of the initial nucleic acid duplex of step(a), said target nucleic acid strand being single- or double-stranded;(c) subjecting the titrated solution to conditions which disrupt theinitial nucleic acid duplex of step (a) and any duplex or triplex formedbetween the target strand and the second nucleic acid strand of theinitial nucleic acid duplex of step (a) upon titration in step (b), butwhich do not disrupt the target strand when double-stranded; (d)subjecting the titrated solution to conditions which promote duplex ortriplex formation; and (e) monitoring the titrated solution for changesin the amount of initial nucleic acid duplex formed as a function of theamount of target nucleic acid strand added by measuring changes in FETdonor or acceptor intensity.
 2. A method for screening for nucleic acidduplex stability comprising: (a) producing a solution containing aninitial nucleic acid duplex with a known stability, said initial nucleicacid duplex comprising a first nucleic acid strand labeled with a donorof a FET pair and a second nucleic acid strand labeled with an acceptorof the FET pair, each strand being capable of forming a duplex with adouble-stranded target strand; (b) titrating the double-stranded targetstrand into the solution; (c) subjecting the titrated solution toconditions which disrupt the initial nucleic acid duplex of step (a),the double-stranded target strand, and any duplex between disruptedtarget strands and the first and second nucleic acid strands of theinitial nucleic acid duplex of step (a); (d) subjecting the titratedsolution to conditions which promote duplex formation; and (e)monitoring the titrated solution for changes in the amount of initialnucleic acid duplex formed as a function of the amount ofdouble-stranded target nucleic acid strand added by measuring changes inFET donor or acceptor intensity.
 3. A method for detecting a singlenucleotide polymorphism comprising: (a) producing an initial nucleicacid duplex comprising a first and second nucleic acid strand, whereinthe first or second strand of the initial nucleic acid duplex isdesigned to identify a single nucleotide polymorphism in a single- ordouble-stranded target nucleic acid sequence and wherein the firstnucleic acid strand comprises a donor nucleic acid strand labeled with adonor of a FET pair and the second nucleic acid strand comprises anacceptor nucleic acid strand labeled with an acceptor of the FET pair;(b) measuring FET donor or acceptor intensity indicative of the amountof the initial nucleic acid duplex produced in step (a); (c) adding afixed excess amount of the single- or double-stranded target nucleicacid strand into the solution; (d) subjecting the solution to conditionswhich disrupt the initial nucleic acid duplex of step (a) and any duplexor triplex formed between the single- or double-stranded target strandand the first or second nucleic acid strand of the initial nucleic acidduplex of step (a) upon addition of the single- or double-strandedtarget strand in step (c), but which do not disrupt the target strandwhen double-stranded; (e) subjecting the titrated solution to conditionswhich promote duplex or triplex formation; and (f) measuring FET donoror acceptor intensity indicative of the amount of initial nucleic acidduplex formed after addition of the single- or double-stranded targetstrand wherein the measured amount after addition of the single- ordouble-stranded target strand is indicative of the single- ordouble-stranded target strand containing the single nucleotidepolymorphism.
 4. A method for detecting a single nucleotide polymorphismcomprising: (a) producing an initial nucleic acid duplex comprising afirst and second nucleic acid strand, wherein the first or second strandof the duplex is designed to identify a single nucleotide polymorphismsin a double-stranded target nucleic acid sequence and wherein the firstnucleic acid strand comprises a donor nucleic acid strand labeled with adonor of a FET pair and the second nucleic acid strand comprises anacceptor nucleic acid strand labeled with an acceptor of the FET pair;(b) measuring FET donor or acceptor intensity indicative of the amountof the initial nucleic acid duplex; (c) adding a fixed excess amount ofthe double-stranded target nucleic acid strand into the solution; (d)subjecting the solution to conditions which disrupt the initial nucleicacid duplex of step (a), the double-stranded target nucleic acidsequence and any duplex formed between the double-stranded target strandand the first or second nucleic acid strand of the initial nucleic acidduplex of step (a) formed upon addition of the double-stranded targetstrand in step (c); (e) subjecting the titrated solution to conditionswhich promote duplex formation, and (f) measuring FET donor or acceptorintensity indicative of the amount of initial duplex formed afteraddition of the target strand wherein the measured amount after additionof the target strand is indicative of the target strand containing thesingle nucleotide polymorphism.
 5. A method for determining theconcentration of a target nucleic acid sequence comprising: (a) adding aknown volume and concentration of an initial nucleic acid duplex with aknown stability to a known volume of a solution containing a targetstrand, said initial nucleic acid duplex comprising a first nucleic acidstrand having a sequence wholly or in part homologous to the targetstrand and labeled with a donor of a FET pair and a second nucleic acidstrand having a sequence wholly or in part complementary to the targetstrand and labeled with an acceptor of the FET pair; (b) subjecting thesolution to conditions which disrupt the initial nucleic acid duplex ofstep (a) and any duplex between the target strand and the first nucleicacid strand or the second nucleic acid strand of the initial nucleicacid duplex of step (a); (c) subjecting the solution to conditions whichpromote duplex formation; and (d) determining the relative change in theamount of initial nucleic acid duplex formed in the solution bymeasuring changes in FET donor or acceptor intensity.
 6. A method fordetermining the concentration of a target nucleic acid sequencecomprising: (a) adding a known volume of a solution of target strand toa known volume of a solution containing a known concentration of aninitial nucleic acid duplex with a known stability, said initial nucleicacid duplex comprising a first nucleic acid strand having a sequencewholly or in part homologous to the target strand and labeled with adonor of a FET pair and a second nucleic acid strand having a sequencewholly or in part complementary to the target strand and labeled with anacceptor of the FET pair; (b) subjecting the solution to conditionswhich disrupt the initial nucleic acid duplex and any duplex between thetarget strand and the first or second nucleic acid strand of the initialnucleic acid duplex; (c) subjecting the solution to conditions whichpromote duplex formation; and (d) determining the relative change in theamount of initial nucleic acid duplex formed in the solution bymeasuring changes in FET donor or acceptor intensity.
 7. A method forassessing stability of various selected target strands comprising: (a)selecting various target strands; (b) performing the method of claim 1with the same initial nucleic acid duplex and each of the selectedtarget strands; and (c) comparing monitored changes in the amount ofinitial nucleic acid duplex formed as a function of the amount of theselected target nucleic acid strand added by measuring changes in FETdonor or acceptor intensity to ascertain differences in stability ofduplexes or triplexes formed by the various target strands.